Conventional in-floor electrical fittings such as floorboxes and poke-through devices often include a cover with two major pieces: a cover ring and a lid. One such conventional fitting is shown in FIGS. 1A and 1B. FIG. 1A is a front view of a conventional fitting 10 and FIG. 1B is a top view of fitting 10. In fitting 10, the lid 14 of cover 12 is mounted to the cover ring 16 through a hinge 18. The cover ring 16 includes an outer flange 20. Outer flange 20 helps to support the fitting against its own weight, as the hole in the floor through which the fitting passes may be slightly larger in diameter than the fitting such that there is insufficient or no friction between the outer surface of the side of the fitting and the inner surface of the hole in the floor. The outer flange 20 extends radially outward from the top portion of the cover ring 16 such that the top surface of the outer flange 20 is flush with the top surface of the lid 14 when the lid 14 is closed. As such, when the fitting is installed in a floor the entire top surface of the outer flange 20 is visible, which is undesirable. Additionally, because the outer flange 20 is integral to the cover ring 16 and extends outwardly from the cover ring in a cantilever-type fashion, there can be appreciable shear stress at the junction between the outer flange 20 and the rest of the cover ring 16, especially when the outer flange is supporting most or all of the weight of the fitting. One type of an in-floor electrical fitting is shown in U.S. Pat. No. 8,063,317.